The Inquisitio Eliensis, or Ely Inquisition, usually abbreviated IE, is one of the major Domesday satellites. It describes the lands of the abbey of Ely in six counties, spread among three different circuits. Although the surviving text is a twelfth-century copy, the general consensus is that it is a copy rather than an updated or 'improved' version of the original text.
The Ely Inquisition is important for several different reasons. It is the only satellite text which deals with the lands of a single tenant-in-chief in several circuits; it is one of only two texts to name Domesday jurors (the other is the Inquisitio Comitatus Cantabrigiensis); it reveals that slaves were recorded in circuit 6 where Domesday Book omits them; and, finally, it purports to list the Articles of Inquiry of the Domesday Inquest.
For more detail, see R. Welldon Finn, 'The Inquisitio Eliensis reconsidered', English Historical Review, vol. 75 (1960), pages 385-409; and V.H. Galbraith, The making of Domesday Book (1961).